Question: 13: When light propagates through a material medium of relative permittivity \varepsilon_{r} and relative permeability \mu_{r}, the velocity of light, v is given by ( c-velocity of light in vacuum)
(1) v=\sqrt{\frac{\varepsilon_{r}}{\mu_{r}}}
(2) v=\frac{c}{\sqrt{\varepsilon_{r} \mu_{r}}}
(3) v=c
(4) v=\sqrt{\frac{\mu_{r}}{\varepsilon_{r}}}
Answer: Option (2)
Explanation:
The speed of light in a medium depends on the electrical and magnetic properties of the medium.
In vacuum, the speed of light is given by
c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}},
where \mu_0 is the permeability of free space and
\varepsilon_0 is the permittivity of free space.
In a material medium, the permeability and permittivity are given by
\mu = \mu_r \mu_0 and \varepsilon = \varepsilon_r \varepsilon_0.
The speed of light in the medium is
v = \frac{1}{\sqrt{\mu \varepsilon}}.
Substituting the values of \mu and \varepsilon,
v = \frac{1}{\sqrt{\mu_r \mu_0 \varepsilon_r \varepsilon_0}}.
Rewriting using the expression for c,
v = \frac{c}{\sqrt{\varepsilon_r \mu_r}}.
Hence, the correct expression for the velocity of light in a medium is
\frac{c}{\sqrt{\varepsilon_r \mu_r}}.